There has already been known a so called EFI (electronic fuel injection) type internal combustion engine which has a flow meter for sensing the amount of air introduced into an intake system of the engine. This engine also has a fuel injector for supplying an amount of fuel into the intake system in accordance with the amount of the introduced air in order to maintain a predetermined constant ratio of the amount of air to the amount of fuel. With this type of internal combustion engine an advantage is obtained in that a constant air-fuel ratio of the air-fuel mixture is supplied to the engine combustion chamber irrespective of the engine operating condition. For example, it is possible to keep the air-fuel ratio at an ideal ratio (about 14.0) for the engine, in order to obtain maximum output power and fuel efficiency. This feature of maintaining an ideal air-fuel ratio irrespective of engine operating condition is also advantageous if the engine is provided with catalytic converter in its exhaust system for suppressing toxic emissions from the engine. This is because a catalytic converter effectively eliminates toxic components in the exhaust gas only when the air-fuel ratio of the air-fuel mixture is controlled to be within a predetermined narrow range. For example, if a three way-catalytic converter is used, it is necessary to keep the air-fuel ratio at an ideal ratio for the engine, in order to obtain effective operation of the three-way catalytic converter.
However, it is often desired to supply an air-fuel mixture with an air-fuel ratio other than said ideal ratio when the engine is operating under a particular condition. For example, a rich air-fuel mixture stabilizes the engine idling operation. Further, to obtain a large output power during the time the engine is operating under high load conditions, a rich air-fuel mixture should be supplied to the engine.